Fluid motion can be dominated either by viscous effects that smooth disturbances or by inertia that allows disturbances and mixing to persist. The Reynolds number compares these influences:

$$Re=\frac{\rho uL}{\mu}=\frac{uL}{\nu}.$$

Here $u$ is a characteristic velocity and $L$ a characteristic length chosen for the flow geometry.

Laminar flow

At sufficiently low Reynolds number, many flows are laminar: fluid motion is smooth and neighboring layers mix relatively little.

Turbulent flow

At sufficiently high Reynolds number, many flows become turbulent, with irregular fluctuations, eddies and strong mixing across a wide range of scales.

Transition depends on the problem

There is no universal Reynolds number that separates all laminar and turbulent flows. The critical range depends on geometry, disturbances and boundary conditions. Pipe flow, boundary layers and flow around bodies therefore use different characteristic lengths and transition criteria.

Dynamic similarity

Two geometrically similar flows with the same relevant dimensionless parameters can exhibit similar behaviour even when their physical size, speed or fluid differ.